In Ruddyoak, I have "Red River Valley"
In Goblin, I have "As the World Falls Down"
In AHS, I have "House of the Rising Sun" (because of Season 3: Coven, which was set in New Orleans, and used that song in its promos)
I made all three of those using sheet music as a guide.
In my old cycle town of Lawndale, I had the "Daria" theme song ("You're Standing on My Neck")
In my old cycle town of Ostara, I had "This Is the Song That Never Ends," which was kind of mean because then the villagers people got from me would sing that song to them.
I had both of those songs written down in my old Population Growing strategy guide, so I don't remember if I made them or not.